A plane wave considered earlier in chapter 2, Eq. (2.1), extends over all space. This wave has a single wave number k and is spread over all space. If we use this plane wave then the particle may be found anywhere in space with equal probability. In this case ∆x = ∞ and ∆px = 0. However, particles are localized in space. If we want to associate a wave with a particle in a consistent way, then the wave-like phenomenon should be localized in the neighbourhood of the particle. That is, we wish to construct a localized wave with nonzero amplitude in a small region of space and zero elsewhere. Such a description of a localized particle can be achieved by constructing a wave packet.